June 18, 1997
Dear Lars,
I agree with much of what you say, and like to elaborate
a little on it.
Indeed there will always be good reasons for having different
types of models - both cochlear and psychoacoustic, both
``physical'' and ``functional.'' In fact, it all depends on
the purpose one has in mind to use a model for. If the target
is a detailed understanding of low-level auditory mechanisms,
then go for the physical route, applying brute-force computing to
solve the many (partial) differential equations. If the target is
efficient simulation, e.g., needed to pull through many complex
sounds at or near the (hearing) system level, then opt for a
functional model, even a ``black-box'' one if it is too hard
to derive a simplified but still accurate functional model from
the physical one (and quite often it *is* too hard).
An advantage of functional models is also that it is often
easier to switch off particular effects, allowing one to
trace which modelled non-ideality causes a certain observed
(functional) effect at the macroscopic level. With physical
models it is often far more difficult to create, say, a given,
measured, nonlinear distortion level: functional models are
sometimes even more accurate than physical model in representing
observable effects, because many parameters in a physical model
are often only approximately known, while in a functional model
distortion itself may be a parameter. The opposite can also
happen, of course, with (too) simple functional models being
(much) less accurate than the physical ones. Furthermore,
functional models may have poor predictive value for ``new''
auditory phenomena: they are better for application areas in
which the range of relevant auditory phenomena is already
known/spanned. In other words, functional models can be
quite good at ``interpolation'' of data sets, but are often
poor at ``extrapolation.''
Another issue is that a model alone is not much good.
Models need to be provided with testbenches, i.e., data
sets to allow comparison of results from different models,
(in)validation of model outcomes for functional versus
physical models, etc. Such testbenches must obviously be
mutually compatible: a single testbench must be usable
with a variety of models.
In my recent draft experiments with the AIM model at
http://ourworld.compuserve.com/homepages/Peter_Meijer/aumodel.htm
I used a .wav file that I would like to see processed by
both physical and functional models of different origins
in order to compare the results. Of course this data set
should have been much larger, e.g., with samples that
cover specific effects of temporal/frequency masking.
Once the physical and functional models give similar
outcomes under a wide variety of data sets (sound waves),
not just few example cases - or they must be very carefully
selected, confidence will grow that each type of model is
good for its particular target area (e.g., understanding
versus efficiency).
I haven't seen a systematic approach to this so far.
[A moment ago the posting from John Beerends came in
while I was finishing this text. I think his detailed
comments are consistent with what I remarked above
about the possible high accuracy of functional models.]
Best wishes,
Peter Meijer